Problem: You are given an integer N.

Construct any one N-by-N matrix a that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem.

* 1 \leq a_{i,j} \leq 10^{15}
* a_{i,j} are pairwise distinct integers.
* There exists a positive integer m such that the following holds: Let x and y be two elements of the matrix that are vertically or horizontally adjacent. Then, {\rm max}(x,y) {\rm mod} {\rm min}(x,y) is always m.

Constraints

* 2 \leq N \leq 500

Input

Input is given from Standard Input in the following format:


N


Output

Print your solution in the following format:


a_{1,1} ... a_{1,N}
:
a_{N,1} ... a_{N,N}

Output

Print your solution in the following format:


a_{1,1} ... a_{1,N}
:
a_{N,1} ... a_{N,N}

Example

Input

2


Output

4 7
23 10

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

typedef long long int int64;
int64 p[1503];
int pn;
int n;
int main()
{
	scanf("%d",&n);
	int i = 2;
	while(pn < 1500) {
		for(int j = 2;j * j <= i;++j) if(i % j == 0) goto isp;
		p[pn++] = i;
		isp:
		++i;
	}
	for(int i = 0;i < n;++i) {
		for(int j = 0;j < n;++j) {
			int64 val;
			if(((i+j)&1) == 1) {
				val = p[(i+j-1)/2] * p[(i+j+1)/2] * p[(i-j-1)/2+2*n] * p[(i-j+1)/2+2*n] + 1;
			} else {
				val = p[(i+j)/2] * p[(i-j)/2+2*n];
			}
			printf("%lld ", val);
		}
		printf("\n");
	}
}